Supercritical Flow

A total of 49 extended abstracts are included in this volume of papers presented at the 15th International Workshop on Water Waves and Floating Bodies, held 17 February - 1 March, 2000, Caesarea, Israel. Also see http://www.eng.tau.ac.il/-miloh/iwwwfb. The objective of the Workshop is to provide a forum for informal discussions of fundamental research, of mutual interest to both engineers and scientists, in the broad area of wave interactions with fixed, floating or submerged bodies.

A series of laboratory experiments in a 6 m long chute using glass particles of mean diameter 100 μm were performed to investigate the interaction of a supercritical, granular flow with obstacles. It was found that the collision of the flow with a row of mounds led to the formation of a jet, whereby a large fraction of the flow was launched from the top of the mounds and subsequently landed back on the chute. The retarding effect of the mounds was investigated quantitatively by direct measurements of the velocity of the flow, its runout length and the geometry of the jet. The effects of several aspects of the layout of the mounds on their retarding effects were examined. It was observed that a row of steep mounds with an elongated shape in the transverse direction to the flow and with a height several times the flow depth led to dissipation of a large proportion of the kinetic energy of the flow.

Recent experience gained at AFRL with the injection of cryogenic fluids into high back-pressures is summarized. In the experimental investigations described, a jet of a cryogenic fluid, typically liquid N2, is injected into a chamber whose ambient pressure is varied to values exceeding the critical pressure of the injectant. The structure of the jet and the shear layer between the jet and the ambient has been examined. Results from visualization, jet growth rate, fractal analysis, and Raman scattering measurements indicate that the behavior of the injected fluid changes from spray-like behavior to gas jet-like behavior as pressure increased.

A series of laboratory experiments in a 6 m long chute using glass particles of mean diameter 100 μm were performed to investigate the interaction of a supercritical, granular flow with obstacles. It was found that the collision of the flow with a row of mounds led to the formation of a jet, whereby a large fraction of the flow was launched from the top of the mounds and subsequently landed back on the chute. The retarding effect of the mounds was investigated quantitatively by direct measurements of the velocity of the flow, its runout length and the geometry of the jet. The effects of several aspects of the layout of the mounds on their retarding effects were examined. It was observed that a row of steep mounds with an elongated shape in the transverse direction to the flow and with a height several times the flow depth led to dissipation of a large proportion of the kinetic energy of the flow.

A new algorithm for the solution of the shallow water equations is introduced. The formulation is founded on a suitable operator-splitting procedure for which a characteristic-based rational form of including balancing dissipation terms is achieved.In the semi-explicit form the method circumvents the requirement of a critical time step given in terms of the wave celerity, which is restrictive for the analysis of long-wave propagation in shallow waters.In this work the robustness of the algorithm is illustrated for transient shallow water problems and for some supercritical flows, where the choice of an algorithm with optimal diffusion properties is manifest.

Ternary phase equilibrium data are presented for acetic acid-water mixtures with supercritical carbon dioxide at temperatures of 313 and 323 K and pressures of 73, 104 and 139 bar. Selectivities and distribution coefficients were obtained from these data and are also reported. Results ...

A non-reacting-flow experimental investigation was undertaken to gain a better understanding of some of the underlying physics associated with the interaction of acoustic waves and a coaxial-jet injector similar to those used in cryogenic liquid rockets. Liquid nitrogen (the round inner jet) and gaseous nitrogen (the annu-lar outer jet) were used under subcritical, near critical, and supercritical chamber pressures, with and with-out acoustic excitation. High-speed digital imaging provided information on the dynamic behavior of the jet under a variety of conditions. It is found that when the jet is at the pressure node, an externally-imposed acoustic field excites the dark-core of the jet to a wavy-shaped structure consistent with the field's charac-teristics. Mean and root mean square (RMS) values of the dark-core length fluctuations were measured from images. It is seen that as the outer-to-inner-jet velocity ratio increases, the RMS of the dark-core length fluctuations decrea...

This technical note studies the supercritical junction flow occurring at the right-angled confluence of four equal-width channels in which two upstream channels carry flow towards the junction. The note seeks to investigate, firstly, the pertinence of a 2D shallow water equation model to reproduce the typical flow structures at the junction. The second objective is to build a computationally efficient model with more resolution applied at critical point i.e. junction and less in areas where the flow is primarily 1D i.e. channels and compare such model, named, ‘sparse’ with a uniformly meshed model regarding solution accuracy and computational efficiency. The results indicate that the sparse model is able to reproduce typical flow structures appearing at the channel junction in an adequate manner. The discharge distribution is fairly well predicted. The jump angles are almost the same in the two models as well as the location and size of the recirculation zones and the flow depth super-elevation areas. However, the two models diverge in the prediction of very small depths in the recirculation zone where the sparse model overestimates the depths. As regards, computational efficiency, the sparse model is found to be 61% more efficient than the uniform mesh model.

Se estudiaron alternativas de diseño para la rápida curva de un aliviadero mediante la complementación entre modelación física y matemática, en la que el principal fenómeno de análisis fueron las ondas cruzadas generadas bajo el régimen de escurrimiento supercrítico. Pueden distinguirse dos estados de funcionamiento para el aliviadero; si el caudal es menor a 220 m 3 /s, la erogación se produce a través de un vertedero de perfil que descarga frontalmente sobre una rápida de pendiente variable y desarrollo curvo; por encima de este caudal entra en funcionamiento un vertedero lateral de perfil triangular, lo cual altera el las características de aproximación del flujo a la rápida. Inicialmente se estudió el diseño original en modelo físico. Debido a la formación de las ondas cruzadas, los niveles del pelo de agua en las paredes de la rápida no resultaban admisibles por generar desborde. Es por ello que se evaluaron dos alternativas con distintos grados de peralte en la curva y modific...

The weakly nonlinear dynamics of long waves embedded in marginally stable shear flows that vary in the streamwise direction are shown to be governed by a variable-coefficient Boussinesq equation. Depending on the local stability characteristics of the flow, new nonmodal or modal instabilities may emerge that serve as natural mechanisms for achieving amplitude thresholds necessary for weakly nonlinear instability and the transition to fully finite-amplitude states.

: An experimental study on the effects of an externally-imposed transverse acoustic field in a N2 shear coaxial jets at sub-, near-, and supercritical pressures is presented. Such fields and their interaction with the jets (i.e., breakup, mixing, etc.) are believed to play a critical role during combustion instabilities in liquid rocket engines. The shear coaxial injector used here is similar to those used in cryogenic liquid rockets. By using N2 as the working fluid, the chemistry effects on combustion instability are separated from the effects of a transverse acoustic field on coaxial jets. Furthermore, through this choice, ambiguities associated with composition dependence on mixtures critical properties are eliminated. The acoustic field is generated by a piezo-siren and the first resonant frequency is ~3kHz. The pressures in the chamber range from 215-716 psia to span subcritical to supercritical pressures. The outer to inner jet velocity ratio varies from ~1.2 to 23 and the mo...

A series of laboratory experiments in a 6 m long chute using glass particles of mean diameter 100 mum were performed to investigate the interaction of a supercritical, granular flow with obstacles. It was found that the collision of the flow with a row of mounds led to the formation of a jet, whereby a large fraction of the flow

ABSTRACT Experimental analysis concerning supercritical flow over a dentated sill in nonsubmerged conditions and the local scour downstream of this sill is presented. In this case, the energy dissipation is incomplete so that a scour control downstream of the hydraulic structure could be required. The use of this type of dissipation device could be needed in cases where the maximum flow depth upstream of the sill must be limited to satisfy physical or structural conditions. This could happen, for instance, in the restoration of stilling basin in gravity dams and at the outlet of diversion systems. Experimental and theoretical results, useful in the design of this type of stilling basin and scour control, are presented in the paper, with an application to the case of the Molato Dam in Italy. DOI: 10.1061/(ASCE)HY.1943-7900.0000407. (C) 2011 American Society of Civil Engineers.

We present estimates of internal shear rates of real-scale avalanches that are based on velocity measurements. Optical velocity sensors installed on the instrument pylon at the Swiss Vallée de la Sionne test site are used to measure flow velocities at different flow heights of three large dry and wet snow avalanches. Possible sources of error in the correlation analysis of the time-lagged reflectivity signals measured by optical sensors are identified for real-size avalanches. These include spurious velocities due to noise and elongated peaks. An appropriate choice of the correlation length is essential for obtaining good velocity estimates. Placing restrictions on the maximum possible accelerations in the flow improves the analysis of the measured data. Coherent signals are found only in the dense flowing cores. We observe the evolution of shear rates at different depths between the front and tail of the flowing avalanche. At the front, large shear rates are found throughout the de...

RESUMEN: El diseño de descargadores de fondo es el resultado de la evaluación conjunta de múltiples aspectos. En ese contexto, la traza de un descargador de fondo aguas abajo de una compuerta podría seguir una curva, por lo que el flujo supercrítico provocará ondas cruzadas que se propagarán hasta la estructura de disipación. Dado que el túnel se encuentra confinado en altura, dichas ondas podrían interactuar con la clave modificando el patrón de ondas y sus consecuencias sobre la estructura. Este trabajo presenta una evaluación del descargador de fondo con un túnel aguas abajo de sección baúl de solera plana, con una curvatura relativa menor a 0,10 y un ángulo de 27,9°, y números de curva comprendidos entre 0,84 y 1,83, analizándose el patrón de ondas cruzadas, la incidencia sobre la clave y las condiciones de disipación mediante salto de esquí. Los resultados obtenidos muestran una incidencia importante del escalón aireador. En los escenarios con solera continua, sin aireador, se aprecia un efecto marcado de la clave del túnel sobre los niveles máximos y el ángulo para los que estos se alcanzan, siempre que el nivel alcance este sector, siendo más significativo este efecto mientras mayor resulte el nivel de embalse. ABSTRACT: The design of bottom outlet structures is the result of the joint evaluation of multiple aspects. In this context, the axis of a bottom outlet downstream a gate may follow a curve, so the supercritical flow will generate cross-waves that propagate until reaching the dissipation structure. Since the tunnel is confined in height, these waves could interact with the upper part by modifying the wave pattern and its influence on the structure. This work presents an evaluation of the outlet bottom into a trunk section tunnel of flat bottom with relative curvature less than 0.10 and an angle of 27.9°, and curve numbers between 0.84 and 1.83, being analyzed the cross-wave pattern, the impact on the upper section and dissipation conditions. The results show a significant effect of aerator. When continuous bottom was considered, an effect of the upper part of the tunnel on the maximum and the angle for those values is appreciated if water elevation goes until this sector, being more important this effect for higher reservoir levels. PALABRAS CLAVES: Flujo supercrítico, curvas, descargadores de fondo.

Two forced convection film boiling correlations are proposed for Fuel Coolant Interaction codes: one for fuel drops in premixing and explosion, and one for fuel fragments in explosion. They include features which are not always taken into account in existing correlations such as for example the Epstein and Hauser correlation: the existence of a stable and an unstable film boiling sub-regime, and inertial and convective effects in the vapor film. Also, a special care has been taken to correctly extrapolate and validate the correlation for fragments in supercritical conditions. The two correlations are built by combining a correlation for high subcoolings and a correlation for low subcoolings, which are chosen among existing or modified correlations. Regarding the film boiling sub-regimes, it is shown that when considering fuel drops both sub-regimes must be taken into account while we may assume that fuel fragments are always in the stable sub-regime. Regarding inertial and convective effects, it is shown that they should be taken into account in both correlations, and that it can be done by using the modified latent heat L' = L + 0.5CpVmΔTsup. It is also shown that using L' instead of L is essential to correctly extrapolate a correlation to supercritical conditions. Indeed, in this case, L' = 0.5CpVmΔTsup is the analogue of a pseudo-latent heat. The correlation for fragments was then compared to the TREPAM data. It was able to predict almost all data within a +/-25 % margin. Finally, in order to further validate the correlation for fragments in supercritical conditions, comparisons were made with numerical simulations with water and with experimental data with carbon dioxide. The correlation performed very well in both cases.

In a previous report, we have presented the argon nanojet injection simulation results under vacuum condition. This study also focused on the effect of injector shape on jet breakup behavior. However, geometrical effects were not so prominent. After a thorough analysis, we concluded that the temperature of the liquid in the solid injector is the governing factor for subsequent nanojet breakup characteristics. We will introduce this conclusion with detailed description in the following section. In addition, the previous nanojet injection code was modified for injection under sub/supercritical pressure. These results will also be presented later in this report.